JP2007170904A - Method for evaluating seismic response of building on improved foundation - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for evaluating more precisely and simply than before the equivalent sharing velocity of the improved foundation corresponding to improvement geometry. <P>SOLUTION: The method for evaluating seismic response of building is performed as follows: a seismic response of building on the original foundation is obtained (S1); whether the response of the building is less than the designed value or not is checked (S2); if less than the designed value, detail design is performed on the original foundation (S3); if exceeding the designed value, improved geometry, rate of improving of the foundation, and strength of the improved foundation are set (S4); an equivalent sharing wave velocity VH of the improved foundation is calculated by using previously prepared equivalent sharing velocity graph (S5); and the seismic response of the building on the improved foundation is obtained (S6). It is checked whether response of the building is less than the designed value or not (S7); if less than the designed value, the detail design of the building on the improved foundation is performed (S8); if the response of the building is exceeding the designed value, improved geography, rate of improving of the foundation and the strength of the improved foundation are set again (S4); and steps following to the S5 are performed again. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an earthquake response evaluation method for a building on an improved ground.

In order to control the settlement of buildings or to suppress the response of buildings during earthquakes, the use of cement mixing ground improvement methods (deep mixing treatment methods) is increasing.
Since this method can improve the ground with an arbitrary improved shape, the improved shape differs depending on the purpose and foundation type. For example, in the case of a solid foundation or pile foundation, the ground is generally improved in a lattice shape and footing is performed. At the foundation, it is performed to improve the shape immediately below the footing into a columnar shape or a block shape.

There exists patent document 1 as a prior art document which improves the ground of the foundation ground which supports a structure. According to Patent Document 1, a ground-impermeable impermeable wall that is divided into a planar grid that penetrates through a sand layer ground that may be liquefied and continues to the bottom of the sand layer ground that does not have the possibility of liquefaction. And a technique for forming a foundation frame of a structure on the ground consolidated impermeable wall is disclosed.
Japanese Patent Laid-Open No. 10-46619

When the ground is improved in a grid shape for the purpose of reducing the building response during an earthquake, the response reduction effect of the ground improvement is often evaluated from the shear wave velocity of the improved ground. In many cases, the shear wave velocity of the ground improvement body is obtained by averaging the areas.
On the other hand, when modifying the footing directly below the footing for the purpose of building settlement control, changes in the dynamic characteristics of the ground due to ground improvement were often not evaluated positively.
In the improved ground, there should be an equivalent shear wave velocity corresponding to the improved shape. However, conventionally, there has been no method for quantitatively evaluating the equivalent shear wave velocity, and thus the above method is simply used. For this reason, a method for accurately and simply evaluating the equivalent shear wave velocity of the improved ground according to the improved shape has been demanded.

  The present invention has been made in view of the above-described problems, and an object of the present invention is to provide a method for accurately and simply evaluating the equivalent shear wave velocity of the improved ground according to the improved shape as compared with the conventional case.

  In order to achieve the above object, the present invention provides a correlation between an equivalent shear wave velocity VH of an improved ground in which a ground improvement body is periodically arranged in plan view in the original ground and the ground improvement rate of the improved ground. An equivalent shear wave velocity graph is used to evaluate the seismic response of a building constructed on the improved ground, wherein the improved ground is a unit period consisting of the ground improved body and the original ground in a predetermined region. Considering an aggregate of structures, the equivalent elastic matrix CH of the improved ground is obtained using equation (1), and the equivalent shear elastic modulus GH of the improved ground, which is a component of the equivalent elastic matrix CH, is used (2) An equivalent shear wave velocity VH of the improved ground is calculated from an equation, and the equivalent shear wave velocity graph is created based on the calculated equivalent shear wave velocity VH of the improved ground.

Where C: elastic matrix of the unit periodic structure, I: unit matrix, X: response displacement vector when unit macro strain is applied to the unit periodic structure, y: microscale, Y: the unit periodic structure Body area, ρ: Average density of the improved ground Here, the ground improvement rate is the area of the ground improved body / the total area of the improved ground. The unit macro distortion means that the average distortion of the improved ground is 1.

Usually, in the improved ground, the ground improvement bodies are periodically arranged in plan view in the original ground, and the improved ground is regarded as an assembly of unit periodic structures consisting of the ground improvement body in a predetermined area and the original ground. Can do. For example, in the case of columnar improvement, as shown in FIG. 9 (a), a single columnar ground improvement body 1 and an original ground 2 in a predetermined region surrounded by a two-dot chain line surrounding it are defined as a unit periodic structure U. Can be considered. Further, in the case of lattice improvement, as shown in FIG. 9B, the original ground 2 and the cross-shaped ground improvement body 11 in a predetermined area surrounded by a two-dot chain line are regarded as a unit periodic structure U. be able to.
On the other hand, when the object is composed of periodic repetitions of basic cells, the material properties of the object can be derived using a mathematical homogenization method (hereinafter simply referred to as the homogenization method). The homogenization method introduces two coordinate systems, micro-scale and macro-scale, and can analyze the distribution of variables in the microstructure as well as the macro characteristics by solving the governing equations of both. Here, when the dimension of the basic cell has an order of ε, the macro scale x and the micro scale y are defined by y = x / ε.

Considering the improved ground as an object and considering the unit periodic structure as a basic cell constituting the object, the equivalent elastic matrix CH of the improved ground can be obtained by the equation (1). The elastic matrix C and the response displacement vector X of the unit periodic structure can be obtained mechanically or analytically, and by substituting them into the equation (1), the equivalent elastic matrix CH of the improved ground is calculated.
When the equivalent elastic matrix CH of the improved ground is calculated, the equivalent shear wave velocity VH of the improved ground can be calculated from the equation (2) using the equivalent shear elastic modulus GH of the improved ground which is a component of the equivalent elastic matrix CH. it can.

  Therefore, for each improved shape such as columnar improvement or grid improvement (shear wave velocity of ground improvement body / shear wave velocity of original ground), the equivalent shear wave velocity VH of the improved ground and the ground improvement rate of the improved ground By creating an equivalent shear wave velocity graph that shows a correlation with the earthquake, it is possible to evaluate the seismic response of the building constructed on the improved ground according to the improved shape more accurately and simply than before. .

  In the seismic response evaluation method for buildings on the improved ground according to the present invention, the equivalent shear wave velocity VH of the improved ground corresponding to the improved shape is calculated using the homogenization method, and the equivalent shear wave velocity graph based on that is used. Since the seismic response of the building constructed on the improved ground is evaluated, the seismic response of the building constructed on the improved ground corresponding to the improved shape can be evaluated more accurately and simply than before.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is an equivalent shear wave velocity graph of the improved ground in the case of columnar improvement, and FIG. 2 is an equivalent shear wave velocity graph of the improved ground in the case of grid improvement. In addition, a in the figure is (shear wave velocity of the ground improvement body / shear wave velocity of the original ground).

  When creating an equivalent shear wave velocity graph of the improved ground, it is necessary to first select an improved shape such as a columnar improvement or a lattice improvement. Next, a and the ground improvement rate are set, and the elastic matrix C and response displacement vector X of the unit periodic structure are obtained mechanically or analytically, and the equivalent elastic matrix CH of the improved ground is calculated using equation (3). To do. Then, the equivalent shear wave velocity VH of the improved ground is calculated from the equation (4) using the equivalent shear elastic modulus GH of the improved ground obtained as a component of the equivalent elastic matrix CH.

  In the following, the equivalent shear wave velocity VH of the improved ground is calculated by sequentially changing a and the ground improvement rate, and the correlation between the equivalent shear wave velocity VH of the improved ground and the ground improvement rate of the improved ground is calculated using a as a parameter. By obtaining the curve group shown, an equivalent shear wave velocity graph corresponding to the selected improved shape can be obtained.

  When using the equivalent shear wave velocity graph shown in FIG. 1 or FIG. 2, first set the equivalent ground wave velocity VH of the improved ground / the shear wave velocity of the original ground, and use the equivalent shear wave velocity graph to The combination of a and ground improvement rate will be selected from a design viewpoint. For example, in the case of columnar improvement, if the equivalent shear wave velocity VH of the improved ground is set to about 1.4 times that of the original ground, the ground improvement rate should be 35% in the range of a = 4 to 20 from FIG. I understand.

Next, the procedure of the seismic response evaluation method for buildings on the improved ground using the equivalent shear wave velocity graph will be described.
FIG. 3 is a flowchart for explaining the procedure of the seismic response evaluation of the building on the improved ground.
First, the earthquake response of the building on the original ground is obtained using a program such as SHAKE according to the one-dimensional overlapping reflection theory (S1). Then, it is checked whether or not the response of the building is equal to or less than the design value (S2). If the response is equal to or less than the design value, the detailed design of the building is performed with the original ground (S3).
If the response of the building exceeds the design value, the ground shall be improved, and the improved shape, ground improvement rate, strength of the ground improvement body, etc. are set (S4), and the equivalent shear wave previously created After calculating the equivalent shear wave velocity VH of the improved ground using the velocity graph (S5), the earthquake response of the building on the improved ground is obtained using a program such as SHAKE (S6). And it is checked whether the response of a building is below a design value (S7), and when it is below a design value, the detailed design of the building on an improved ground is performed (S8).
When the response of the building exceeds the design value, the improved shape, the ground improvement rate, the strength of the ground improvement body, etc. are reset (S4), and the steps after S5 are performed again.

Now, the method for calculating the equivalent shear wave velocity VH of the improved ground according to the improved shape using the homogenization method has been described, but it is necessary to clarify the accuracy thereof. In the following, we will verify the accuracy of this method by taking an example of a centrifugal loading test conducted by creating an experimental model of improved ground.
4 to 6 show experimental models used in the centrifugal load test. 4 shows a columnar improvement model, FIG. 5 shows a lattice improvement model, and FIG. 6 shows a non-improvement model. Each figure also shows an accelerometer ACC, a displacement meter LDT, and a bender element BE, and the acceleration, displacement, and shear wave velocity of each part of the experimental model were measured. The bender element BE is used for measuring the shear wave velocity, and includes a pair of piezoelectric elements having functions of an oscillator and a receiver.

  FIG. 7 shows the values measured by the bender element BE for the shear wave velocity of the raw ground 2 constituting each experimental model. In the figure, a square mark indicates a columnar improved model, a triangular mark indicates a lattice improved model, and a black circle indicates an unimproved model. Further, the solid line and the broken line are the shear wave velocities of the original ground 2 modeled when the homogenization method is used. These values are obtained by correcting the measured shear wave velocity according to the shear strain amount of the ground at the time of resonance. On the other hand, the shear wave velocity of the ground improvement bodies 1 and 11 is 650 m / s.

In the centrifugal load test, an experimental model such as a construction or ground is set on a vibrating table at the tip of a rotating arm, and an earthquake is generated in the experimental model on the vibrating table in a state where the model is rotated at a high speed. By applying a centrifugal force that is tens of times the gravity of the experimental model, the apparent weight of the experimental model increases proportionally, so the properties of the actual ground can be reproduced. By adjusting the rotation speed of the arm according to the scale of the actual construction or ground and the experimental model, it is possible to conduct model experiments on buildings and grounds of various sizes.
In this test, the rotating arm was rotated at a high speed of 30 G, and the input acceleration for each experimental model was set to 3 G or 5 G, and a sine wave sweep test was performed between 30 and 300 Hz.

  Table 1 compares the experimental results with the eigenvalue analysis results for the primary natural frequency of each experimental model. Here, the eigenvalue analysis is calculated by the shear type model shown in FIG. 8 from the equivalent shear elastic modulus GH of each experimental model estimated using the homogenization method and the average density ρ of the improved ground. The experimental results and the eigenvalue analysis results are almost consistent, and it can be seen that the vibration characteristics of the improved ground can be evaluated with high accuracy by using the homogenization method.

  Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and can be appropriately changed without departing from the spirit thereof. For example, in the above embodiment, examples of the columnar improvement and the lattice improvement are shown as the improved ground, but it goes without saying that the present invention can be applied to other improved shapes.

It is an equivalent shear wave velocity graph of the improved ground in the case of columnar improvement. It is an equivalent shear wave velocity graph of the improved ground in the case of lattice improvement. It is a flowchart for demonstrating the procedure of the earthquake response evaluation method of the building on the improved ground which concerns on this invention. The experimental model (columnar improvement model) of a centrifugal-force loading test is shown, (a) is the standing sectional view, (b) is a plane sectional view. The experimental model (grid-like improvement model) of a centrifugal loading test is shown, (a) is the standing sectional view, and (b) is a plan sectional view. The experimental model (non-improved model) of a centrifugal load test is shown, (a) is the elevation sectional view, (b) is a plane sectional view. It is the graph which showed the shear wave velocity of the original ground used for the centrifugal loading test. It is a schematic diagram of an eigenvalue analysis model. The partial top view of an improved ground is shown, (a) is a case of columnar improvement, (b) is a case of lattice-like improvement.

Explanation of symbols

1,11 Ground improvement body 2 Original ground U Unit periodic structure ACC Accelerometer LDT Displacement meter BE Bender element

Claims (1)

Using the equivalent shear wave velocity graph showing the correlation between the equivalent shear wave velocity VH of the improved ground in which the ground improvement body is periodically arranged in the original ground in plan view and the ground improvement rate of the improved ground, A method for evaluating an earthquake response of a building constructed on the improved ground,
The improved ground is regarded as an assembly of unit periodic structures composed of the ground improved body and the original ground in a predetermined region, and an equivalent elastic matrix CH of the improved ground is obtained using the equation (1), and the equivalent elastic matrix CH The equivalent shear wave velocity VH of the improved ground is calculated from the equation (2) using the equivalent shear elastic modulus GH of the improved ground, which is a component of A method for evaluating the seismic response of buildings on improved ground, characterized by creating an equivalent shear wave velocity graph.

Where C: elastic matrix of the unit periodic structure, I: unit matrix, X: response displacement vector when unit macro strain is applied to the unit periodic structure, y: microscale, Y: the unit periodic structure Body area, ρ: average density of the improved ground

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